The invention provides acrylic hot-melt adhesive compositions which exhibit little change in melt viscosity, excellent hot-melt applicability, and excellent initial cohesion before moisture curing and are excellent in pressure-sensitive adhesiveness and high-temperature cohesion after moisture curing. The invention relates to an acrylic block copolymer characterized by consisting of acrylic polymer blocks (A) and (B) which are different in glass transition temperature range and having at least one crosslinking group (X) at an end; and reactive hot-melt adhesive compositions containing the block copolymer.